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1. One leg of a right triangle decreases at 1 in./min. and the other leg increases at 2 in./min. At what rate is the area changing when the first leg is 8 inches and the second leg is 6 inches?

1. One leg of a right triangle decreases at 1 in./min. and the other leg increases at 2 in./min. At what rate is the area changing when the first leg is 8 inches and the second leg is 6 inches?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve the following time rates problems. 1. One leg of a right triangle decreases at 1 in./min. and the other leg increases at 2 in./min. At what rate is the area changing when the first leg is 8 inches and the second leg is 6 inches? 2. A light shines on top of a lamppost 30 feet above the ground. A woman 5 feet tall walks away from the light. Find the rate at which her shadow is increasing if she is walking at 3 ft/s. 3. A (right circular) cylinder is expanding in such a way that its height is increasing three times as rapidly as the radius of its base. At the moment when its height is 5 inches and the radius of its base is 3 inches its height is increasing at a rate of 12 inches per minute. At that moment its volume is increasing at a rate of cubic inches per minute. 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm wide of 50 cm. If the through leaks water at the rate of 2000 cm3/min, how fast is the water level decreasing when the water is 20 cm deep. 5. A kite 100 feet above the ground is being blown away from the person holding its string in a direction parallel to the ground and at a rate of 10 feet per second. At what rate must the string be let out when the length of string already let out is 200 feet?
Transcribed Image Text:Solve the following time rates problems. 1. One leg of a right triangle decreases at 1 in./min. and the other leg increases at 2 in./min. At what rate is the area changing when the first leg is 8 inches and the second leg is 6 inches? 2. A light shines on top of a lamppost 30 feet above the ground. A woman 5 feet tall walks away from the light. Find the rate at which her shadow is increasing if she is walking at 3 ft/s. 3. A (right circular) cylinder is expanding in such a way that its height is increasing three times as rapidly as the radius of its base. At the moment when its height is 5 inches and the radius of its base is 3 inches its height is increasing at a rate of 12 inches per minute. At that moment its volume is increasing at a rate of cubic inches per minute. 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm wide of 50 cm. If the through leaks water at the rate of 2000 cm3/min, how fast is the water level decreasing when the water is 20 cm deep. 5. A kite 100 feet above the ground is being blown away from the person holding its string in a direction parallel to the ground and at a rate of 10 feet per second. At what rate must the string be let out when the length of string already let out is 200 feet?
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